Question 927906
{{{11x^2+17y^2+484x+442y+7636=0}}}

{{{(11x^2+484x)+(17y^2+442y)+7636=0}}}

{{{11(x^2+44x)+17(y^2+26y)+7636=0}}}.............complete square

{{{11(x^2+44x+__)+17(y^2+26y+___)+7636=0 }}}

{{{11(x^2+44x+_22^2_)-11*22^2+17(y^2+26y+_13^2__)-17*13^2+7636=0 }}}

{{{11(x+22)^2-5324+17(y+13)^2)-2873+7636=0 }}}

{{{11(x+22)^2+17(y+13)^2)-8197+7636=0 }}}

{{{11(x+22)^2+17(y+13)^2)-561=0 }}}

{{{11(x+22)^2+17(y+13)^2)=561}}}

{{{(11561)/(x+22)^2+(17/561)(y+13)^2)=561/561}}}

{{{(x+22)^2/51+(y+13)^2)/33=1}}}

ellipse

center is at ({{{-22}}},{{{-13}}})

{{{a=sqrt(51)}}}..=>..{{{a=7.14143}}} semimajor axis length

{{{b=sqrt(33)}}}..=>..{{{b=5.74456}}} semiminor axis length


foci | (({{{-22-3sqrt(2)}}},{{{ -13}}})  |  ({{{-22+3 sqrt(2)}}}, {{{-13}}})),approx.(({{{-26.2426}}}, {{{-13}}})  |  ({{{-17.7574}}}, {{{-13}}}))
vertices | (({{{-22-sqrt(51)}}}, {{{-13}}})  |  ({{{-22+sqrt(51)}}}, {{{-13}}})),approx.(({{{-29.1414}}}, {{{-13}}})  |  ({{{-14.8586}}}, {{{-13}}}))

focal parameter | {{{11/sqrt(2)}}}, approx. {{{7.77817}}}
eccentricity | {{{sqrt(6/17)}}},approx. {{{0.594089}}}


 {{{ graph( 600, 600, -34, 34, -35, 35,-sqrt(-33(x+22)^2/51+33)-13 ,sqrt(-33(x+22)^2/51+33)-13) }}}